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October  2007, 1(4): 597-613. doi: 10.3934/jmd.2007.1.597

A note on Reeb dynamics on the tight 3-sphere

Frédéric Bourgeois 1, , Kai Cieliebak 2, and  Tobias Ekholm 3,

1. 

Département de Mathématique, Université Libre de Bruxelles CP 218, Boulevard du Triomphe, 1050 Bruxelles, Belgium
2. 

Mathematisches Institut der LMU München, Theresienstr. 39, 80333 München, Germany
3. 

Department of Mathematics, Uppsala University, Box 480, 751 06 Uppsala, Sweden

Received  March 2007 Revised  July 2007 Published  July 2007

We show that a nondegenerate tight contact form on the 3-sphere has exactly two simple closed Reeb orbits if and only if the differential in linearized contact homology vanishes. Moreover, in this case the Floquet multipliers and Conley-Zehnder indices of the two Reeb orbits agree with those of a suitable irrational ellipsoid in 4-space.
Keywords: Reeb dynamics, contact homology, periodic orbit..
Mathematics Subject Classification: Primary: 57R58; Secondary: 57R17, 35B1.
Citation: Frédéric Bourgeois, Kai Cieliebak, Tobias Ekholm. A note on Reeb dynamics on the tight 3-sphere. Journal of Modern Dynamics, 2007, 1 (4) : 597-613. doi: 10.3934/jmd.2007.1.597
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